An efficient multi-fidelity space-division assisted optimization approach for computationally expensive problems

This paper presents a multi-fidelity optimization approach for computationally expensive problems, aiming to efficiently find the global optimum by utilizing MF models. Firstly, high-fidelity (HF) and low-fidelity (LF) samples are selected and calculated, respectively. Subsequently, the design space is categorized into four types based on the responses of the HF and LF samples: overlapped subspace, HF promising subspace, merged subspace, and global space. These defined spaces are explored alternately to find the global optimum. To further reduce computational expenses, a correlation analysis process is introduced to determine whether the HF or LF model should be used as the objective function in the present subspace. To avoid missing the global optima, both local exploitation and global exploration strategies are employed in these subspaces. The proposed method named multi-fidelity space-division assisted optimization (MFSDO) is compared with four popular methods using twenty-three mathematical test problems, results demonstrate that MFSDO offers advantages in reducing computational costs. Additionally, MFSDO is applied to optimize the structure of a blended-wing-body underwater glider. Results indicate that the structure mass is significantly reduced with much less computational cost while ensuring safety, which verifies the efficiency and engineering applicability of our proposed method.